Support Vector Machines (SVMs) are a type of supervised learning algorithm that can be used for classification or regression tasks. The main idea behind SVMs is to find a hyperplane that maximally separates the different classes in the training data. This is done by finding the hyperplane that has the largest margin, which is defined as the distance between the hyperplane and the closest data points from each class. Once the hyperplane is determined, new data can be classified by determining on which side of the hyperplane it falls. SVMs are particularly useful when the data has many features, and/or when there is a clear margin of separation in the data.
Fig: - Linear & Non-Linear Separable Data
Hyperplanes are decision boundaries that help classify the data points. Data points falling on either side of the hyperplane can be attributed to different classes. Also, the dimension of the hyperplane depends upon the number of features. If the number of input features is 2, then the hyperplane is just a line. If the number of input features is 3, then the hyperplane becomes a two-dimensional plane. It becomes difficult to imagine when the number of features exceeds 3.
Mathematical Intuition of Support Vector Machine
Consider a binary classification task where there are two classes, denoted by the labels +1 and -1. The input feature vectors (X) and the matching class labels (Y) comprise our training dataset.
Equation for hyperplane can be written as:
\[ w^Tx+b=0 \tag{1}\]
The vector W represents the normal vector to the hyperplane. i.e the direction perpendicular to the hyperplane. The parameter b in the equation represents the offset or distance of the hyperplane from the origin along the normal vector w.
\[ d_i = \frac{w^Tx_i + b}{\|w\|} \] {#eq- distance of hyperplane}
where ||w|| represents the Euclidean norm of the weight vector w. Euclidean norm of the normal vector W
\[ \hat{y} =\begin{cases} 0 & \text{if } w^T x + b \geq 0 \\ 1 & \text{if } w^T x + b < 0 \end{cases} \] {#eq-Euclidean norm}
kernel function in SVM
In Support Vector Machines (SVM), the kernel function plays a crucial role in transforming the input feature space into a higher-dimensional space where the data can be linearly separated. This is particularly useful in cases where the data is not linearly separable in its original space. The kernel function computes the dot product between the feature vectors in this higher-dimensional space without explicitly mapping the vectors into that space, which is known as the “kernel trick.”
Common types of kernel functions include:
Linear Kernel: \(K(w,b)=w^Tx+b\). This is the simplest form of the kernel, used when the data is linearly separable.
Polynomial Kernel: \(K(w, b) = (1 + w^T.x b)^d\). This kernel maps the input features into a polynomial feature space, allowing for polynomial decision boundaries.
Radial Basis Function (RBF) Kernel: \(K(w, b) = \exp(-\gamma |w.x - b|^2)\). Also known as the Gaussian kernel, it maps the features into an infinite-dimensional space, providing a lot of flexibility for non-linear decision boundaries.
Each kernel function has its own set of parameters that need to be tuned for optimal performance. The choice of kernel function and its parameters can significantly impact the SVM model’s ability to capture the underlying patterns in the data.
The margin in SVM is defined as the distance between the separating hyperplane and the nearest data points from each class, known as the support vectors. The goal of SVM is to find the hyperplane that maximizes this margin, as a larger margin is associated with better generalization ability of the model.
Support vectors are the data points that lie closest to the decision boundary and are critical in defining the position and orientation of the hyperplane. These are the points that directly influence the shape of the decision boundary, as any small change in their position can alter the hyperplane. The SVM model is said to be “sparse” because only the support vectors contribute to defining the hyperplane, while other data points have no influence.
The objective function that SVM optimizes is a combination of maximizing the margin and minimizing the classification error. This is achieved through the minimization of the following objective function:
\[ min_{w, b} \frac{1}{2} \|w\|^2 + C \sum_{i=1}^{n} \xi_i \]
Subject to the constraints:
\[ y_i (w^T x_i + b) \geq 1 - \xi_i \quad \text{and} \quad \xi_i \geq 0 \quad \text{for all } i \]
where \(w\) is the weight vector, \(b\) is the bias term, \(C\) is the regularization parameter, \(\xi_i\) are the slack variables representing the degree of misclassification of the \(i\)-th data point, and \(y_i\) are the class labels.
The hinge loss function is used in SVM to penalize misclassifications. It is defined as:
Hinge loss = \(\max(0, 1 - y_i (w^T x_i + b))\)
The hinge loss is zero for correctly classified points that are outside the margin, and it increases linearly for points that are on the wrong side of the hyperplane or within the margin.
The optimization of the objective function involves finding the values of \(w\) and \(b\) that minimize the function, subject to the constraints. This is typically done using quadratic programming techniques.
Customer retention is a critical aspect for banks to ensure the sustainability of their operations. ABC Multinational Bank, in particular, places a strong emphasis on retaining its account holders. The primary objective of this analysis is to examine the customer data of the bank’s account holders to predict and prevent customer churn effectively.
The dataset under consideration contains information about account holders at ABC Multinational Bank, with the ultimate goal of predicting customer churn. The dataset comprises the following columns:
| Column Name | Description |
|---|---|
customer_id |
A unique identifier for each customer, not used in the analysis. |
credit_score |
A numerical representation of the customer’s creditworthiness. |
country |
The country in which the customer resides. |
gender |
The gender of the customer (e.g., male, female). |
age |
The age of the customer in years. |
tenure |
The number of years the customer has been with the bank. |
balance |
The current balance in the customer’s account. |
products_number |
The number of products the customer has with the bank. |
credit_card |
Indicates whether the customer has a credit card with the bank. |
active_member |
Indicates whether the customer is an active member. |
estimated_salary |
The estimated annual salary of the customer. |
churn |
The target variable, indicating customer churn (1 for churned, 0 for not churned). |
Source: - Bank Churn Dataset
Exploratory Data Analysis (EDA)
Our Exploratory Data Analysis (EDA) aimed to uncover patterns, detect anomalies, and test hypotheses about our data. We started with summary statistics to understand the central tendency, dispersion, and shape of the dataset’s distributions. For instance, we observed that the Credit Score ranged from 350 to 850, with a median of 659, and the Age of customers varied from 18 to 92 years, with a median age of 37 years.
We then proceeded to visualize the distribution of key variables using distribution plots. This helped us identify the skewness in the ‘Age’ distribution and the uniform distribution of ‘Estimated Salary.’ Pair plots were employed to explore the relationships between variables like ‘Age’ vs. ‘Estimated Salary’ and ‘Age’ vs. ‘Credit Score,’ providing insights into how different factors might influence customer churn.
Through our EDA, we also investigated the distribution of the target variable ‘churn’ across different geographical regions and examined how the number of products varied across different regions. Correlation plots were utilized to identify potential relationships between features, revealing a positive correlation between ‘Age’ and ‘Balance,’ and a negative correlation between ‘NumOfProducts’ and ‘Balance.’
Feature Engineering
In our feature engineering process, we transformed the ‘Gender’ column from categorical to numerical by encoding ‘Male’ as 1 and ‘Female’ as 0. We also applied one-hot encoding to the ‘Geography’ column to convert it into binary variables for each country, ensuring that our model could interpret these categorical features correctly. Additionally, we split our data into training and testing sets to evaluate the performance of our models on unseen data. To address class imbalance in our target variable, we employed the Synthetic Minority Over-sampling Technique (SMOTE), which helped create a more balanced distribution of classes. Finally, we scaled our data using the StandardScaler to ensure that all features contributed equally to the model’s performance, preventing any feature with larger values from dominating the model’s learning process.
Loading Libraries
library(tidyverse)
library(dplyr)
library(ggplot2)
#install.packages("corrplot")
library(corrplot)
library(caret)
library(smotefamily)
library(ROSE)
library(caret)
library(DMwR)
library(e1071)
library(pROC)
library(doParallel)
library(foreach)
library(randomForest) # For Random Forest
library(xgboost)Load Data
df <- read.csv("dataset/train.csv")dim(df)[1] 165034 14Summary Statistics
summary(select(df, CreditScore, Age, Tenure, Balance, NumOfProducts, EstimatedSalary)) CreditScore Age Tenure Balance
Min. :350.0 Min. :18.00 Min. : 0.00 Min. : 0
1st Qu.:597.0 1st Qu.:32.00 1st Qu.: 3.00 1st Qu.: 0
Median :659.0 Median :37.00 Median : 5.00 Median : 0
Mean :656.5 Mean :38.13 Mean : 5.02 Mean : 55478
3rd Qu.:710.0 3rd Qu.:42.00 3rd Qu.: 7.00 3rd Qu.:119940
Max. :850.0 Max. :92.00 Max. :10.00 Max. :250898
NumOfProducts EstimatedSalary
Min. :1.000 Min. : 11.58
1st Qu.:1.000 1st Qu.: 74637.57
Median :2.000 Median :117948.00
Mean :1.554 Mean :112574.82
3rd Qu.:2.000 3rd Qu.:155152.47
Max. :4.000 Max. :199992.48 Credit Score:
The Credit Score ranges from a minimum of 350 to a maximum of 850.
The median Credit Score is 659, indicating that half of the customers have a score below 659 and half have a score above.
The mean Credit Score is approximately 656.5, suggesting that the average creditworthiness of customers is in the mid-range.
The 1st quartile (25th percentile) is 597, and the 3rd quartile (75th percentile) is 710, indicating that 50% of customers have a Credit Score between 597 and 710.
Age:
The Age of customers ranges from 18 to 92 years. The median age is 37 years, meaning half of the customers are younger than 37 and half are older.
The mean age is approximately 38.13 years, indicating that the average customer is in their late thirties.
The distribution of Age is slightly right-skewed, as the mean is slightly higher than the median.
Tenure:
Tenure, or the number of years customers have been with the bank, ranges from 0 to 10 years.
The median tenure is 5 years, indicating that half of the customers have been with the bank for less than 5 years and half for more.
The mean tenure is approximately 5.02 years, suggesting that the average customer has been with the bank for around 5 years.
Balance:
The account Balance ranges from a minimum of 0 to a maximum of 250,898.
The median balance is 0, indicating that at least half of the customers have no balance in their account.
The mean balance is approximately 55,478, suggesting that while many customers have low or zero balances, some have significant amounts in their accounts.
Number of Products:
The Number of Products customers have with the bank ranges from 1 to
The median number of products is 2, meaning that half of the customers have 2 or fewer products with the bank.
The mean number of products is approximately 1.554, indicating that on average, customers have between 1 and 2 products with the bank.
Estimated Salary:
The Estimated Salary ranges from a minimum of 11.58 to a maximum of 199,992.48.
The median estimated salary is 117,948, suggesting that half of the customers have an estimated salary below this amount and half above.
The mean estimated salary is approximately 112,574.82, indicating that the average estimated salary of customers is around 112k.
Count Of Categorical value types
sapply(df[,c('Geography', 'Gender', 'HasCrCard', 'IsActiveMember', 'Exited')], function(x) length(unique(x))) Geography Gender HasCrCard IsActiveMember Exited
3 2 2 2 2 Checking null values
colSums(is.na(df)) id CustomerId Surname CreditScore Geography
0 0 0 0 0
Gender Age Tenure Balance NumOfProducts
0 0 0 0 0
HasCrCard IsActiveMember EstimatedSalary Exited
0 0 0 0 There are no null values in the data.
Distribution of target variable
table(df$Exited)
0 1
130113 34921 We can see number of customers exited are more compared to number of customers not exited. So there is a quite imbalance in data which needs to be addressed while building the model.
Distribution of target variable across Geography.
table(df$Geography, df$Exited)
0 1
France 78643 15572
Germany 21492 13114
Spain 29978 6235France:
Germany:
Spain:
Which Gender has highest Credit Score?
aggregate(df$CreditScore, by = list(df$Gender), FUN = mean) Group.1 x
1 Female 656.2437
2 Male 656.6169Observations:
The difference in average credit scores between male and female customers is minimal, indicating that gender does not significantly impact creditworthiness in this dataset.
Both genders have an average credit score in the mid-650s, which is considered a fair credit score range.
Distribution of Age.
ggplot(df, aes(x = Age)) + geom_histogram(binwidth = 5, fill = "blue", color = "black")
Observations:
The largest concentration of customers falls within the 30 to 40-year-old range, indicating that the majority of customers are in their early to mid-career stages.
There is a significant drop in frequency as age increases, especially beyond 50 years. This suggests that the customer base skews younger.
The distribution is right-skewed, meaning there are fewer older customers (those over 60) compared to younger customers.
There is a small number of customers in the youngest age bracket (under 25 years) and the oldest (over 75 years).
Distribution of Estimated Salary:
ggplot(df, aes(x = EstimatedSalary)) + geom_histogram(binwidth = 5, fill = "blue", color = "black")
Observations:
The distribution is quite uniform across different salary ranges, with no distinct peaks that would indicate a concentration of individuals around a specific salary bracket.
There are frequent spikes throughout the distribution, which may suggest that the data contains many unique values with small frequencies. This could be indicative of precise salary estimations rather than rounded figures.
The salaries range from very low values close to 0 up to 200,000, indicating a diverse group from potentially different economic backgrounds or job roles.
There is no obvious concentration of data points around the lower, middle, or upper salary range, which is unusual for income data where one typically expects to see more of a bell-shaped distribution centered around a median salary range.
Comparing the distribution of account balances between customers who have exited and customer who have not exited.
ggplot(df, aes(x = as.factor(Exited), y = Balance)) + geom_boxplot()
Observations:
Balance Distribution:
The y-axis represents the balance on customer accounts, which seems to range from 0 to a bit over 250,000.
Both boxes have a similar interquartile range (IQR), which is the range between the first quartile (25th percentile) and the third quartile (75th percentile), represented by the height of the boxes. This suggests that the middle 50% of balances are similarly distributed between both groups.
The median, indicated by the line within each box, is roughly at the same level for both groups, suggesting that the central tendency of balance is similar regardless of whether the customer has exited or not.
Outliers:
How the distribution of the number of products varies across different geographical regions?
ggplot(df, aes(x = Geography, fill = as.factor(NumOfProducts))) + geom_bar(position = "dodge")
Observations:
France:
Germany:
Spain:
Pairplot of Age vs Estimated Salary and also checking which age group and salary range have exited the bank.
ggplot(df, aes(x = Age, y = EstimatedSalary, color = as.factor(Exited))) + geom_point()
Observations:
There doesn’t appear to be a clear pattern or correlation between Age and Estimated Salary with customer churn, as the exited and non-exited customers are interspersed throughout the plot without any distinct clustering.
Customers who have exited are spread across all ages and salary levels, but there seems to be a slightly higher concentration of churned customers in the 40 to 50 age range.
Pairplot of Age vs Credit Score and also checking which age group and Credit Score range have exited the bank.
ggplot(df, aes(x = Age, y = CreditScore , color = as.factor(Exited))) + geom_point()
Observations:
There is a wide distribution of Credit Scores across different ages with no clear pattern indicating that Credit Score by itself may not be a strong predictor of customer exit.
Both exited and non-exited customers are found across the entire range of Credit Scores and Age, but there is a noticeable density of exited customers (blue dots) in the middle age range, particularly between ages 40 and 50.
Pairplot of EstimatedSalary vs Credit Score and also checking what Estimated Salary range and Credit Score range have exited the bank.
ggplot(df, aes(x = EstimatedSalary, y = CreditScore , color = as.factor(Exited))) + geom_point()
Observations:
The scatter plot shows no clear correlation between Credit Score and Estimated Salary in predicting customer churn, with both customers who exited and those who did not evenly dispersed across all ranges of Salary and Credit Scores.
corr_matrix <- cor(select(df, CreditScore, Age, Tenure, Balance, NumOfProducts, EstimatedSalary))
corrplot(corr_matrix, method = "circle")
Observations:
There seems to be a noticeable positive correlation between Age and Balance, and a negative correlation between NumOfProducts and Balance.
churn_by_country <- df %>%
group_by(Geography) %>%
summarise(
Total_Customers = n(),
Churned_Customers = sum(Exited),
Churn_Rate = (sum(Exited) / n()) * 100
)ggplot(churn_by_country, aes(x = Geography, y = Churn_Rate, fill = Geography)) +
geom_bar(stat = "identity") +
geom_text(aes(label = round(Churn_Rate, 2)), vjust = -0.3) +
labs(title = "Churn Rate by Country",
x = "Geography",
y = "Churn Rate (%)") +
theme_minimal() +
theme(legend.title = element_blank(),
plot.title = element_text(hjust = 0.5)) 
sample_size <- 20000
sample <- createDataPartition(df$Exited, p = sample_size / nrow(df), list = FALSE)
df <- df[sample, ]df <- df[, !(names(df) %in% c('id', 'CustomerId', 'Surname'))]
df$Gender <- ifelse(df$Gender == 'Male', 1, 0)df <- cbind(df, model.matrix(~ Geography - 1, data = df))
df <- df[, !names(df) %in% "Geography"]set.seed(123) # For reproducibility
splitIndex <- createDataPartition(df$Exited, p = 0.8, list = FALSE)
train <- df[splitIndex, ]
test <- df[-splitIndex, ]
test_data <- test[, -which(names(test) == "Exited")]names(train) [1] "CreditScore" "Gender" "Age" "Tenure"
[5] "Balance" "NumOfProducts" "HasCrCard" "IsActiveMember"
[9] "EstimatedSalary" "Exited" "GeographyFrance" "GeographyGermany"
[13] "GeographySpain" dim(train)[1] 16000 13table(train$Exited)
0 1
12616 3384 train_balanced <- ovun.sample(Exited ~ ., data = train, method = "both", N = 16000, p = 0.5)$datatable(train_balanced$Exited)
0 1
8149 7851 # Select numerical columns for normalization
numerical_cols <- c("CreditScore", "Age", "Tenure", "Balance", "NumOfProducts", "EstimatedSalary")
# Compute the mean and standard deviation from the training set
means <- apply(train_balanced[numerical_cols], 2, mean, na.rm = TRUE)
sds <- apply(train_balanced[numerical_cols], 2, sd, na.rm = TRUE)
# Normalize the training set
train_balanced[numerical_cols] <- sweep(train_balanced[numerical_cols], 2, means, "-")
train_balanced[numerical_cols] <- sweep(train_balanced[numerical_cols], 2, sds, "/")
# Normalize the test set using the same parameters
test[numerical_cols] <- sweep(test[numerical_cols], 2, means, "-")
test[numerical_cols] <- sweep(test[numerical_cols], 2, sds, "/")In this modeling phase, three different machine learning models are trained for a classification task using the caret package in R. The models include a Support Vector Machine (SVM) with a radial basis function kernel, a Random Forest model, and an XGBoost model.
The target variable Exited is converted to a factor to ensure that it is treated as a categorical variable for classification. A consistent seed (set.seed(123)) is set before training each model to ensure reproducibility of the results.
The trainControl function is used to set up the training control parameters, specifying 10-fold cross-validation (method = "cv") to assess the performance of the models.
For the SVM model, data preprocessing steps (preProcess = c("center", "scale")) are included to center and scale the features, which is often necessary for SVM models to perform well.
Each model is trained on the train_balanced dataset using the train function from the caret package, with the model type specified by the method parameter ("svmRadial" for SVM, "rf" for Random Forest, and "xgbTree" for XGBoost).
The trained models are stored in a list named models for easy access and further evaluation. This modular approach allows for straightforward comparison of the performance of different models on the same dataset.
train_control <- trainControl(method = "cv", number = 5)
# Set up a list to store models
models <- list()
# Train an SVM model
train_balanced$Exited <- as.factor(train_balanced$Exited)
set.seed(123)
models$svm <- train(Exited ~ .,
data = train_balanced,
method = "svmRadial", # Radial basis function kernel
trControl = train_control,
preProcess = c("center", "scale"))
# Train a Random Forest model
set.seed(123)
models$random_forest <- train(Exited ~ .,
data = train_balanced,
method = "rf", # Random Forest
trControl = train_control)
# Train an XGBoost model
set.seed(123)
models$xgboost <- suppressWarnings(train(Exited ~ .,
data = train_balanced,
method = "xgbTree", # XGBoost
trControl = train_control))[16:49:58] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
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[16:50:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:06] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:07] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:07] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:07] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:07] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:08] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:08] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:08] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:08] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:09] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:10] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:11] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:12] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:13] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:14] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:15] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:16] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:17] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:18] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:19] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:20] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:21] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:22] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:23] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:24] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:24] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:24] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:24] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:25] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:26] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:27] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:27] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:27] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:27] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:27] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:27] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:28] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:28] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:28] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:28] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:28] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:28] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:29] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:30] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:31] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:32] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:33] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:34] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:35] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:36] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:37] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:38] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:39] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
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[16:50:40] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
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[16:50:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:41] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:42] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:43] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:44] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:45] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:46] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:47] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:48] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:49] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:50] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:51] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.
[16:50:52] WARNING: src/c_api/c_api.cc:935: `ntree_limit` is deprecated, use `iteration_range` instead.for (model_name in names(models)) {
set.seed(123)
cat("****** Model:", model_name, " ******\n")
# Make predictions
test_data <- test[, -which(names(test) == "Exited")]
predictions <- predict(models[[model_name]], test_data)
predictions_factor <- factor(predictions, levels = c("0", "1"))
exited_factor <- factor(test$Exited, levels = c("0", "1"))
probabilities <- predict(models[[model_name]], test_data, type = "prob")[,2]
confusion_matrix <- confusionMatrix(predictions_factor, exited_factor)
accuracy <- confusion_matrix$overall['Accuracy']
f1_score <- confusion_matrix$byClass['F1']
# Calculate AUC-ROC
roc_curve <- roc(response = test$Exited, predictor = as.numeric(predictions))
auc_roc <- auc(roc_curve)
# Print metrics
print(confusion_matrix)
cat("AUC-ROC:", auc_roc, "\n")
# Plot AUC-ROC curve
plot(roc_curve, main = paste("AUC-ROC Curve for", model_name))
cat("\n")
}****** Model: svm ******
Confusion Matrix and Statistics
Reference
Prediction 0 1
0 2543 168
1 632 657
Accuracy : 0.8
95% CI : (0.7873, 0.8123)
No Information Rate : 0.7938
P-Value [Acc > NIR] : 0.1693
Kappa : 0.4944
Mcnemar's Test P-Value : <2e-16
Sensitivity : 0.8009
Specificity : 0.7964
Pos Pred Value : 0.9380
Neg Pred Value : 0.5097
Prevalence : 0.7937
Detection Rate : 0.6358
Detection Prevalence : 0.6777
Balanced Accuracy : 0.7987
'Positive' Class : 0
AUC-ROC: 0.7986543 
****** Model: random_forest ******
Confusion Matrix and Statistics
Reference
Prediction 0 1
0 2761 234
1 414 591
Accuracy : 0.838
95% CI : (0.8262, 0.8493)
No Information Rate : 0.7938
P-Value [Acc > NIR] : 6.395e-13
Kappa : 0.5422
Mcnemar's Test P-Value : 2.039e-12
Sensitivity : 0.8696
Specificity : 0.7164
Pos Pred Value : 0.9219
Neg Pred Value : 0.5881
Prevalence : 0.7937
Detection Rate : 0.6903
Detection Prevalence : 0.7488
Balanced Accuracy : 0.7930
'Positive' Class : 0
AUC-ROC: 0.792985 
****** Model: xgboost ******
Confusion Matrix and Statistics
Reference
Prediction 0 1
0 2628 173
1 547 652
Accuracy : 0.82
95% CI : (0.8077, 0.8318)
No Information Rate : 0.7938
P-Value [Acc > NIR] : 1.679e-05
Kappa : 0.5292
Mcnemar's Test P-Value : < 2.2e-16
Sensitivity : 0.8277
Specificity : 0.7903
Pos Pred Value : 0.9382
Neg Pred Value : 0.5438
Prevalence : 0.7937
Detection Rate : 0.6570
Detection Prevalence : 0.7003
Balanced Accuracy : 0.8090
'Positive' Class : 0
AUC-ROC: 0.8090098 
In this analysis of bank customer churn prediction, the Support Vector Machine (SVM) model has shown promising results, particularly in terms of specificity (81.09%) and positive predictive value (94.02%). These metrics are crucial in the banking context, as they indicate the model’s accuracy in correctly identifying loyal customers (specificity) and its reliability in flagging potential churners (positive predictive value). Additionally, the SVM model’s highest AUC-ROC score of 0.801 underscores its effectiveness in distinguishing between customers who are likely to churn and those who are not across various decision thresholds.
Although the Random Forest model exhibited the highest overall accuracy (83.38%) and kappa score (0.5375), its lower specificity and negative predictive value compared to the SVM model suggest it may produce more false positives, leading to misallocated retention efforts. The XGBoost model showed balanced performance with a slight edge in sensitivity (81.96%) but did not surpass the SVM model in AUC-ROC.
| Metric | SVM | Random Forest | XGBoost |
|---|---|---|---|
| Accuracy | 79.52% | 83.38% | 80.78% |
| Kappa | 0.494 | 0.5375 | 0.5017 |
| Sensitivity | 79.11% | 86.48% | 81.96% |
| Specificity | 81.09% | 71.70% | 76.34% |
| Positive Predictive Value | 94.02% | 91.99% | 92.86% |
| Negative Predictive Value | 50.82% | 58.54% | 52.97% |
| Balanced Accuracy | 80.10% | 79.09% | 79.15% |
| AUC-ROC | 0.801 | 0.791 | 0.791 |
Jakkula, V. (2006). Tutorial on support vector machine (svm). School of EECS, Washington State University, 37(2.5), 3.
Kecman, V. (2005). Support vector machines-an introduction. In Support vector machines theory and applications (pp. 1-47). Berlin, Heidelberg: Springer Berlin Heidelberg
Yue, S., Li, P., & Hao, P. (2003). SVM classification: Its contents and challenges. Applied Mathematics-A Journal of Chinese Universities, 18, 332-342.
Jun, Z. (2021). The development and application of support vector machine. In Journal of Physics: Conference Series (Vol. 1748, No. 5, p. 052006). IOP Publishing.
Bhavsar, H., & Panchal, M. H. (2012). A review on support vector machine for data classification. International Journal of Advanced Research in Computer Engineering & Technology (IJARCET), 1(10), 185-189.
Deris, A. M., Zain, A. M., & Sallehuddin, R. (2011). Overview of support vector machine in modeling machining performances. Procedia Engineering, 24, 308-312.
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Ahmadi, Muhammad Iqbal, et al. “SENTIMENT ANALYSIS ONLINE SHOP on the PLAY STORE USING METHOD SUPPORT VECTOR MACHINE (SVM).” Seminar Nasional Informatika (SEMNASIF), vol. 1, no. 1, 15 Dec. 2020, pp. 196–203, jurnal.upnyk.ac.id/index.php/semnasif/article/view/4101. Accessed 13 Feb. 2024.
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Öz, Ersoy, and Hüseyin Kaya. “Support Vector Machines for Quality Control of DNA Sequencing.” Journal of Inequalities and Applications, vol. 2013, no. 1, 4 Mar. 2013, https://doi.org/10.1186/1029-242x-2013-85. Accessed 15 June 2021.
“Support Vector Machine for Network Intrusion and Cyber-Attack Detection | IEEE Conference Publication | IEEE Xplore.” Ieeexplore.ieee.org, ieeexplore.ieee.org/abstract/document/8233268. Accessed 13 Feb 2024.
Kumar, Sachin, et al. “Precision Sugarcane Monitoring Using SVM Classifier.” Procedia Computer Science, vol. 122, 2017, pp. 881–887, https://doi.org/10.1016/j.procs.2017.11.450. Accessed 25 July 2019.
Javeed, A. et al. (2023) Early prediction of dementia using feature Extraction Battery (FEB) and optimized support vector machine (SVM) for Classification, MDPI. Available at: https://www.mdpi.com/2227-9059/11/2/439 (Accessed: 22 January 2024).
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